Fast Deterministic Constructions of Linear-Size Spanners and Skeletons
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In the distributed setting, the only existing constructions of sparse skeletons, (i.e., subgraphs with O(n) edges) either use randomization or large messages, or require Ω(D) time, where D is the hop-diameter of the input graph G. We devise the first deterministic distributed algorithm in the CONGEST model (i.e., uses small messages) for constructing linear-size skeletons in time 2^O(√( n· n)). We can also compute a linear-size spanner with stretch polylog(n) in low deterministic polynomial time, i.e., O(n^ρ) for an arbitrarily small constant ρ >0, in the CONGEST model. Yet another algorithm that we devise runs in O( n)^κ-1 time, for a parameter κ=1,2,..., and constructs an O( n)^κ-1 spanner with O(n^1+1/κ) edges. All our distributed algorithms are lightweight from the computational perspective, i.e., none of them employs any heavy computations.
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